Multiples animations in a single blend file
You can save multiple animations (called Actions in Blender) for a rig by using the Dope Sheet and changing its context to Action Editor (switched with a dropdown menu in the Dope Sheet's header). From the Action Editor, each animation can be stored as an Action datablock (the same way you can have multiple mesh or material datablocks).

Important: If you store multiple actions make sure you give each action a fake user by clicking the F button to the right of the Actions datablock in the Action Editor's header. Failure to do so will result in you losing animations after saving and closing Blender. This is because all datablocks without users (including Actions) are purged when a file is saved and reloaded. Giving the action a fake user prevents that from happening.